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Let \(y=y(x)\) be the solution of the differential equation \(\left(x^2-3 y^2\right) d x+3 x y d y=0, y(1)=1\). Then \(6…

Q1

Let \(y=y(x)\) be the solution of the differential equation \(\left(x^2-3 y^2\right) d x+3 x y d y=0, y(1)=1\).
Then \(6 y^2(\mathrm{e})\) is equal to

[JEE Main 2023, 24 Jan (Shift 2)]

a

\(\frac{3}{2} \mathrm{e}^2\)

b

\(\mathrm{e}^2\)

c

\(2 e^2\)

d

\(3 e^2\)

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